(\partial)/(\partial x)(2x^2+y^2-x^2y)

解

\frac{\partial}{\partial x} (2 x^{2} + y^{2} - x^{2} y)

4 x - 2 x y

解答ステップ

\frac{\partial}{\partial x} (2 x^{2} + y^{2} - x^{2} y)

y

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (2 x^{2}) + \frac{\partial}{\partial x} (y^{2}) - \frac{\partial}{\partial x} (x^{2} y)

\frac{\partial}{\partial x} (2 x^{2}) = 4 x

\frac{\partial}{\partial x} (y^{2}) = 0

\frac{\partial}{\partial x} (x^{2} y) = 2 y x

= 4 x + 0 - 2 y x

簡素化

= 4 x - 2 x y